In Fig. REF  four-momentum and constituent background subtraction are compared. To this end a di-jet sample is generated with Jewel 2.3.0 [1]}, [2]} in the standard set-up using the simple medium model described in [2]}. Jets are reconstructed with the anti-\(k_\perp \)  algorithm [4]} and for each the background subtraction is performed twice: once with the four-momentum method and once with constituent subtraction. As seen in the left panel of Fig. REF  the jet's transverse momentum after background subtraction is the same with both methods while the jet axis can move to a slightly different position (central panel in Fig. REF ). The mass difference, however, is clearly asymmetric (right panel in Fig. REF ): the mass with constituent background subtraction is smaller than with four-momentum subtraction (considering only jets with a positive mass squared after four-momentum subtraction). Observables built from the jet's transverse momentum and direction (e.g. the di-jet asymmetry \(A_J\) ) are thus insensitive to details of the background subtraction procedure, while the jet mass is not.
